This is supposed to be good for me

Everyone says it’s helpful/reflective/cathartic/instructive to write about lessons that flopped, and I guess I don’t disagree. But there’s something very uncomfortable, clearly, about seizing upon an idea, envisioning its unfolding in your classroom, doing the [sometimes huge amount of] prep work, and either watching hopelessly as it sinks like a lead balloon or flailing about to keep the ball rolling. (Okay – sorry for the overindulgent metaphors were in that last sentence.) And I’m still not sure the lesson was as complete a disaster as I thought it was. I’ll let you be the judge along with me as I reflectively recount it.

When I read Lisa B’s wonderful post about introducing key vocabulary in her geometry class, I immediately knew that I wanted to try the same thing with my students. She was helpful and generous, sharing her files as well as a step-by-step description of her procedure. We had spent the first four days of class estimating, analyzing visual patterns, preparing our interactive notebooks, and exploring the idea of justification through folding paper. This lesson seemed the perfect way to dig into the content while preserving a cooperative and constructive atmosphere. I created the vocabulary strips with our new laminator (thank you, donorschoose!), photocopied a pile of Frayer Models, and scripted the introduction in my mind. I was ready to go.

The Laminatorrrrr

I had not given out my course contract during the first few days of school because all the other teachers were doing that in their classes, and I couldn’t bear the glazed eyes of students who had heard the same speech 5 times already. But now it was the sixth day of school, the contracts had been returned by the Copy Center (the other reason I hadn’t yet distributed them), and it was getting late to disseminate written expectations. I thought I would do a brief ‘scavenger hunt’ as a class warm-up, highlight the class rules that might not have appeared on other contracts (my famous Rule 0 – No Grooming), and transition directly to the activity. Needless to say, the contract review took longer than I had planned, which is not necessarily a bad thing – expectations should be said out loud in your classroom, even if they have been said in others.

Borrowing shamelessly from Lisa, we successfully completed “What is a Widget?” The students seemed to grasp the idea of example versus counterexample. I modeled how to complete a Frayer model using the word ‘ray’, realizing that they would not be able to define ‘angle’ without that term first. I also realized that many students did not know certain notation conventions – for example, that equal numbers of tick marks on segments or angles signify congruence. I have very patient and cooperative students in my 2nd period class (the first class in which I tried this lesson), and we worked through these kinks together. But by the time they got to work on writing their own definitions, there were less than 15 minutes in the class left.

Despite the warm-up with the Widgets and my modeling, the students seemed reluctant to proceed similarly on their own. Almost every table (there are 8) required a significant amount coaching to write their definitions, and to use the counterexamples in identifying characteristics. I told the students we would jump right into the activity the following day, in the hopes that they would complete at least half the list. I had originally planned having them swap definitions with other groups, but not enough work had been completed for that to be an effective activity.

The following day was Geometry textbook day – determined by my assistant principal, and mandatory. Textbook distribution involves sending a group of students to the book room (two floors down) where they wait in line with students from other Geometry classes, and upon receiving a stack of books, return to the classroom. The students completed their book receipts, got their books, and continued working on vocabulary. I asked them to put the books away and develop their definitions in the same manner as the day before – through discussion and observation. But when I read this definition, I realized that some of the students were using their textbooks, and asked them to stop, repeatedly. Let’s just say, I didn’t get 100% compliance with my request. But with 8 tables and 34 students, I wasn’t able to control this.

By the end of the second class, most of the students were on their second sheet of Frayer models, which meant they had completed at least 6 definitions. I observed that my efforts at getting the students to talk to each other about the vocabulary were only moderately successful, and that some students, who were not engaged in conversation, spent most of their time copying the examples and counterexamples. As I moved around the classroom and talked to the students, I also realized that many of them were missing some of the finer points of the definitions – that supplementary angles did not need to be adjacent, for instance (and defining adjacent – that was a hugely difficult task for most) – and that misconceptions were showing up in some of their work.

Some definitions are better than others…

I collected all of their work (three classes times 34 students times 2 sheets each = a lot of definitions). I brainstormed my next steps with a colleague, who suggested I look for the best definitions from all of the classes, and put together a ‘master’ which the students could use to create the final Frayer models to go into their notebooks – an idea which I think will give credit to the students who understood the activity and provide solutions for those who struggled with it. And it won’t be me spoon-feeding them the definitions, or having them copied directly from the textbook.

But after two class periods and a whole lot of prep (not to mention the work to come), I am not sure what was accomplished. I know that these concepts will need to be re-introduced and carefully reviewed. Have I laid the groundwork for that? Or have I seeded the geometric field with misconceptions? And I’m not sure what I would do differently. Would it have worked better if my classes were smaller? (You know the answer to that – of course, it would have.) Clearly the addition of the contract review and the interruption of textbook distribution distracted from the task at hand.

I want to understand this better, because I don’t want to spend the prep time and energy, as well as the classroom time and energy, on activities that I can’t execute properly, or that may not benefit the kids. If my goal is to guide them through constructing some geometric meaning for themselves (rather than delivering it directly), I want to make sure that they are learning.

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2 comments

At the very least you have prepped them for understanding that there is a whole new vocabulary for math and that to effectively communicate in math you need to be precise in your words and meanings. They’re never going to remember these words until they’re put in action anyway but at least now they’ll have a handy reference guide to check whenever they’re looking for the precise right word to describe what they see. I don’t think all is lost. 🙂